Spanish term (edited): [que ya empezó] a mandar

As I see it, the "false start" comes earlier in the sentence. after Zapatero. Next, there should be a period after "mandar."

Here's my take on it:

"The Zapatero administration--... actually it [what is being discussed] got started (earlier) under Aznar, shortly after he took office. He began negotiations...

Explanation: Aznar's administration ended in 2004; Zapatero took office in March of that year. In case you haven't seen it, I found the following abstract on the subject of your text. It shows the chronology:

Perni, Orietta. "Migration in Spain from Aznar to Zapatero: A Real Change of Direction?" Paper presented at the annual meeting of the International Studies Association, Town & Country Resort and Convention Center, San Diego, California, USA, Mar 22, 2006 <Not Available>. 2009-05-12 <http://www.allacademic.com/meta/p100247_index.html>

Publication Type: Conference Paper/Unpublished Manuscript
Abstract: Spain is considered a new immigration country whereby 7% of its 43 millions inhabitants are immigrants. While this number does not include illegal immigrants because of the difficulty in exacting an accurate number, estimates suggest about 1.5 million of people are non-documented immigrants (43% of the total). **It was with Aznar's administration (1996-2004)** that the Spanish government implemented a new migration policy that has led to a securitization of migration with a very strict migration law thus contributing to the maintenance of 'fortress Europe'. **With the governmental change in March 2004**, expectations have grown about a new migration policy that is more flexible and without criminalization of migrants. Zapatero's administration has begun to formalize the status of 'illegal people' staying in Spain but it is just the first step in managing a very problematic situation. The main aim of this paper is compare the two governments' attitude and understandings about migration and what the effects have been of these at the European and international levels addressing the question: can we speak of a real change of direction in the migration policy of Spain?